Question

Two parallel lines are cut by a transversal, then which of the following are true?
1. Pair of alternate interior angles are congruent.
2. Pair Of corresponding angles are congruent.
3. Pair of interior angles on the same side of the transversal are supplementary.​

Answer 1

Answer:

All the three statements are correct.

Step-by-step explanation:

When two or more lines are cut by a transversal, the angles which occupy the same relative position are called corresponding angles .

In the figure the pairs of corresponding angles are:

∠1 and ∠5, ∠2 and ∠6, ∠3 and ∠7, ∠4 and ∠8

When the lines are parallel, the corresponding angles are congruent .

When two lines are cut by a transversal, the pairs of angles on one side of the transversal and inside the two lines are called the consecutive interior angles .

In the above figure, the consecutive interior angles are:

∠3 and ∠6, ∠4 and ∠5

If two parallel lines are cut by a transversal, then the pairs of consecutive interior angles formed are supplementary .

When two lines are cut by a transversal, the pairs of angles on either side of the transversal and inside the two lines are called the alternate interior angles .

In the above figure, the alternate interior angles are:

∠3 and ∠5, ∠4 and ∠6

If two parallel lines are cut by a transversal, then the alternate interior angles formed are congruent.

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